乘积流形M^n×R中具有非零Neumann边值条件的常平均曲率方程解的存在性和唯一性  

Existence and Uniqueness of Solutions to the Constant Mean Curvature Equation with Nonzero Neumann Boundary Data in Product Manifold M^n×R

作　　者：高雅 毛井 宋春兰 Gao Ya;Mao Jing;Song Chunlan(Faculty of Mathematics and Statistics&Key Laboratory of Applied Mathematics of Hubei Province,Hubei University,Wuhan 430062)

机构地区：[1]湖北大学数学与统计学学院&应用数学湖北省重点实验室,武汉430062

出　　处：《数学物理学报（A辑）》2020年第6期1525-1536,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11801496,11926352);霍英东教育基金会青年教师基金和应用数学湖北省重点实验室基金。

摘　　要：该文证明了乘积流形M^n×R中具有非零Neumann边值条件的常平均曲率方程解的存在性和唯一性,这里M^n是Ricci曲率非负的n维完备黎曼流形,n≥2,R是1维的欧氏空间.等价地,这个结论给出了定义在紧致严格凸域Ω■M^n上的具有非退化Neumann边值条件的常平均曲率图超曲面的存在性.In this paper,we can prove the existence and uniqueness of solutions to the constant mean curvature(CMC for short)equation with nonzero Neumann boundary data in product manifold M^n×R,where M^n is an n-dimensional(n≥2)complete Riemannian manifold with nonnegative Ricci curvature,and R is the Euclidean 1-space.Equivalently,this conclusion gives the existence of CMC graphic hypersurfaces defined over a compact strictly convex domainΩ■M^n and with nonzero Neumann boundary data.

关 键 词：常平均曲率 Neumann边值条件 凸性 RICCI曲率 乘积流形 

分 类 号：O186.1[理学—数学]